DOI

We obtain several new sharp C-continuity conditions, both necessary and sufficient, for operators of harmonic reflection of functions over boundaries of simple Carathéodory domains in RN. These results are based on a new criterion (also obtained in this paper) for C-continuity of the Poisson operator in the aforesaid domains. As corollaries, we give new sufficient conditions for C-approximability of functions by harmonic polynomials on boundaries of simple Carathéodory domains in RN. Bibliography: 17 titles.

Original languageEnglish
Pages (from-to)1159-1170
Number of pages12
JournalSbornik Mathematics
Volume211
Issue number8
DOIs
StatePublished - Aug 2020

    Scopus subject areas

  • Algebra and Number Theory

    Research areas

  • Cm-approximation by harmonic polynomials, Harmonic reflection operator, Lipschitz-Holder spaces, Poisson operator, Simple Carath eodory domain

ID: 86668568